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This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
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Autorenporträt
Elias M. Stein is Professor of Mathematics at Princeton University.
Inhaltsangabe
Preface Guide to the Reader Prologue 3 I Real-Variable Theory 7 II More About Maximal Functions 49 III Hardy Spaces 87 IV H[superscript 1] and BMO 139 V Weighted Inequalities 193 VI Pseudo-Differential and Singular Integral Operators: Fourier Transform 228 VII Pseudo-Differential and Singular Integral Operators: Almost Orthogonality 269 VIII Oscillatory Integrals of the First Kind 329 IX Oscillatory Integrals of the Second Kind 375 X Maximal Operators: Some Examples 433 XI Maximal Averages and Oscillatory Integrals 467 XII Introduction to the Heisenberg Group 527 XIII More About the Heisenberg Group 587 Bibliography 645 Author Index 679 Subject Index 685
Preface Guide to the Reader Prologue 3 I Real-Variable Theory 7 II More About Maximal Functions 49 III Hardy Spaces 87 IV H[superscript 1] and BMO 139 V Weighted Inequalities 193 VI Pseudo-Differential and Singular Integral Operators: Fourier Transform 228 VII Pseudo-Differential and Singular Integral Operators: Almost Orthogonality 269 VIII Oscillatory Integrals of the First Kind 329 IX Oscillatory Integrals of the Second Kind 375 X Maximal Operators: Some Examples 433 XI Maximal Averages and Oscillatory Integrals 467 XII Introduction to the Heisenberg Group 527 XIII More About the Heisenberg Group 587 Bibliography 645 Author Index 679 Subject Index 685
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